SAT Subject Physics Practice Question 200: Answer and Explanation

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Question: 200

46. A sample of an ideal gas is heated, doubling its absolute temperature. Which of the following statements best describes the result of heating the gas?

A. The root-mean-square speed of the gas molecules doubles.
B. The average kinetic energy of the gas molecules increases by a factor of .
C. The average kinetic energy of the gas molecules increases by a factor of 4.
D. The speeds of the gas molecules cover a wide range, but the root-mean-square speed increases by a factor of .
E. The speeds of the gas molecules cover a wide range, but the root-mean-square speed increases by a factor of 2.

Correct Answer: D

Explanation:

From the kinetic theory of gases, we know that the average kinetic energy of the molecules of an ideal gas is directly proportional to the absolute temperature. This eliminates B and C. Furthermore, the fact that KEavgT implies that the root-mean-square speed of the gas molecules, vrms, is proportional to the square root of the absolute temperature. This eliminates A and E.

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